Non-Self-Averaging of a Two-Person Game with Only Positive Spillover: A New Formulation of Avatamsaka’s Dilemma

  • Yuji Aruka
  • Eizo Akiyama


In this game (Aruka 2001), selfishness may not be determined even if an agent selfishly adopts the strategy of defection. Individual selfishness can only be realized if the other agent cooperates, therefore gain from defection can never be assured by defection alone. The sanction by defection as a reaction of the rival agent cannot necessarily reduce the selfishness of the rival. In this game, explicit direct reciprocity cannot be guaranteed. Now we introduce different spillovers or payoff matrices, so that each agent may then be faced with a different payoff matrix. A ball in the urn is interpreted as the number of cooperators, and the urn as a payoff matrix. We apply Ewens’ sampling formula to our urn process in this game theoretic environment.


Repeated Game Payoff Matrix White Ball Positive Spillover Payoff Matrice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Faculty of CommerceChuo UniversityTokyoJapan
  2. 2.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan

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